Welcome to Journal of University of Chinese Academy of Sciences,Today is

›› 2010, Vol. 27 ›› Issue (3): 306-313.DOI: 10.7523/j.issn.2095-6134.2010.3.002

• Review Article • Previous Articles     Next Articles

Nontrivial solutions for semilinear elliptic problems with Hardy-Sobolev critical exponents and a weight

DOU Jing-Bo   

  1. School of Statistics, Xian University of Finance and Economics, Xian 710100, China
  • Received:2009-09-25 Revised:2009-12-14 Online:2010-05-15
  • Supported by:

    Supported by the National Natural Science Foundation of China (10802061) and Natural Science Basic Research Plan in Shaanxi Province of China(SJ08F27) 

Abstract:

Using linking theorem and analytic technique, we discuss the existence of nontrivial solutions for the following semilinear elliptic problem with Hardy-Sobolev critical exponents and weights - Δ u-μ u |x|2 =λu+K(x) |u|2*(s)-2u |x|s , x∈Ω; u=0, x∈Ω, where Ω is an open bounded domain of R <em>N with smooth boundary Ω and 0∈Ω, N≥5, 0<s<2,0≤μ< N-2 2 2, λ>0, and K (x) is a bounded positive function on Ω.

Key words: Hardy-Sobolev critical exponent, semilinear elliptic equation, linking theorem, nontrivial solution

CLC Number: